1.

Record Nr.

UNINA9910460429403321

Autore

Ford William H.

Titolo

Numerical linear algebra with applications : using matlab / / by William Ford

Pubbl/distr/stampa

London, England : , : Academic Press, , 2015

©2015

ISBN

0-12-394784-7

Edizione

[First edition.]

Descrizione fisica

1 online resource (629 p.)

Disciplina

512.5

Soggetti

Algebras, Linear - Data processing

Engineering mathematics - Data processing

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Front Cover; Numerical Linear Algebra with Applications; Copyright; Dedication; Contents; List of Figures; List of Algorithms; Preface; Matrices; Matrix Arithmetic; Matrix Product; The Trace; MATLAB Examples; Linear Transformations; Rotations; Powers of Matrices; Nonsingular Matrices; The Matrix Transpose and Symmetric Matrices; Chapter Summary; Problems; MATLAB Problems; Linear Equations; Introduction to Linear Equations; Solving Square Linear Systems; Gaussian Elimination; Upper-Triangular Form; Systematic Solution of Linear Systems; Computing the Inverse; Homogeneous Systems

Application: A TrussApplication: Electrical Circuit; Chapter Summary; Problems; MATLAB Problems; Subspaces; Introduction; Subspaces of Rn; Linear Independence; Basis of a Subspace; The Rank of a Matrix; Chapter Summary; Problems; MATLAB Problems; Determinants; Developing the Determinant of a 2bold0mu mumu section2 and a 3bold0mu mumu section3 Matrix; Expansion by Minors; Computing a Determinant Using Row Operations; Application: Encryption; Chapter Summary; Problems; MATLAB Problems; Eigenvalues and Eigenvectors; Definitions and Examples; Selected Properties of Eigenvalues and Eigenvectors

DiagonalizationPowers of Matrices; Applications; Electric Circuit; Irreducible Matrices; Ranking of Teams Using Eigenvectors; Computing



Eigenvalues and Eigenvectors using MATLAB; Chapter Summary; Problems; MATLAB Problems; Orthogonal Vectors and Matrices; Introduction; The Inner Product; Orthogonal Matrices; Symmetric Matrices and Orthogonality; The L2 Inner Product; The Cauchy-Schwarz Inequality; Signal Comparison; Chapter Summary; Problems; MATLAB Problems; Vector and Matrix Norms; Vector Norms; Properties of the 2-Norm; Spherical Coordinates; Matrix Norms; The Frobenius Matrix Norm

Induced Matrix NormsSubmultiplicative Matrix Norms; Computing the Matrix 2-Norm; Properties of the Matrix 2-Norm; Chapter Summary; Problems; MATLAB Problems; Floating Point Arithmetic; Integer Representation; Floating-Point Representation; Mapping from Real Numbers to Floating-Point Numbers; Floating-Point Arithmetic; Relative Error; Rounding Error Bounds; Addition; Multiplication; Matrix Operations; Minimizing Errors; Avoid Adding a Huge Number to a Small Number; Avoid Subtracting Numbers That Are Close; Chapter Summary; Problems; MATLAB Problems; Algorithms; Pseudocode Examples

Inner Product of Two VectorsComputing the Frobenius Norm; Matrix Multiplication; Block Matrices; Algorithm Efficiency; Smaller Flop Count Is Not Always Better; Measuring Truncation Error; The Solution to Upper and Lower Triangular Systems; Efficiency Analysis; The Thomas Algorithm; Efficiency Analysis; Chapter Summary; Problems; MATLAB Problems; Conditioning of Problems and Stability of Algorithms; Why Do We Need Numerical Linear Algebra?; Computation Error; Forward Error; Backward Error; Algorithm Stability; Examples of Unstable Algorithms; Conditioning of a Problem

Perturbation Analysis for Solving a Linear System

Sommario/riassunto

Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science.   With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for



2.

Record Nr.

UNINA9910746091903321

Autore

Lecca Paola <1973->

Titolo

Introduction to Mathematics for Computational Biology / / by Paola Lecca, Bruno Carpentieri

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023

ISBN

9783031365669

3031365666

Edizione

[1st ed. 2023.]

Descrizione fisica

1 online resource (268 pages)

Collana

Techniques in Life Science and Biomedicine for the Non-Expert, , 2367-1122

Altri autori (Persone)

CarpentieriB

Disciplina

570.285

Soggetti

Bioinformatics

Biomathematics

Biochemistry

Biology - Technique

Biophysics

Computational and Systems Biology

Mathematical and Computational Biology

Biophysical Methods

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

1. Introduction to graph theory -- 2. Biological networks -- 3. Network inference for drug discovery- 4. Introduction to differential and integral calculus -- 5. Modelling chemical reactions -- 6. Reaction-diffusion systems -- 7. Linear algebra background -- 8. Regression -- 9. Cardiac electrophysiology -- .

Sommario/riassunto

This introductory guide provides a thorough explanation of the mathematics and algorithms used in standard data analysis techniques within systems biology, biochemistry, and biophysics. Each part of the book covers the mathematical background and practical applications of a given technique. Readers will gain an understanding of the mathematical and algorithmic steps needed to use these software tools appropriately and effectively, as well how to assess their specific circumstance and choose the optimal method and technology. Ideal for



students planning for a career in research, early-career researchers, and established scientists undertaking interdiscplinary research. .